Problem: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 3x - 6$ and $ JT = 9x - 36$ Find $CT$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {3x - 6} = {9x - 36}$ Solve for $x$ $ -6x = -30$ $ x = 5$ Substitute $5$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 3({5}) - 6$ $ JT = 9({5}) - 36$ $ CJ = 15 - 6$ $ JT = 45 - 36$ $ CJ = 9$ $ JT = 9$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {9} + {9}$ $ CT = 18$